A high-performance reproducing kernel Hilbert spaces (RKHS) numerical framework is formulated for space–time fractional differential equations (FDEs). Advanced optimization strategies reduce computational complexity from non-local fractional operators, overcoming limitations of traditional reproducing kernel (RK) methods. Dispensing with the complex Gram–Schmidt Orthogonalization (GSO), the framework is easy to implement. Theoretical analyses confirm asymptotic convergence of approximate solutions, and comparative tests validate its superiority in generating high-precision global approximate solutions for space–time FDEs with error accumulation issues. • The method stably yields accurate global approximate solutions for target problems. • The associated computational program has a streamlined, user-friendly architecture. • Large step sizes keep small errors, offering high precision with reduced runtime.
Wang et al. (Fri,) studied this question.